Exhaustion of hyperbolic complex manifolds and relations to the squeezing function

Abstract

The purpose of this article is twofold. The first aim is to characterize an $n$-dimensional hyperbolic complex manifold $M$ exhausted by a sequence $\{{\Omega }_j\}$ of domains in ${\mathbb{C}}^n$ via an exhausting sequence $\{f_j:{\Omega }_j\to M\}$ such that $f_j^{-1}(a)$ converges to a boundary point ${\xi }_0\in \partial \Omega$ for some point $a\in M$. Then, our second aim is to show that any spherically extreme boundary point must be strongly pseudoconvex.

18 pages, 2 figues, we

References in corpus (1)

• Limits of an increasing sequence of complex manifolds